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Discovering the dynamic behavior of unknown systems using fuzzy logic

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Abstract

To know the dynamic behavior of a system it is convenient to have a good dynamic model of it. However, in many cases it is not possible either because of its complexity or because of the lack of knowledge of the laws involved in its operation. In these cases, obtaining models from input–output data is shown as a highly effective technique. Specifically, intelligent modeling techniques have become important in recent years in this field. Among these techniques, fuzzy logic is especially interesting because it allows to incorporate to the model the knowledge that is possessed of the system, besides offering a more interpretable model than other techniques. A fuzzy model is, formally speaking, a mathematical model. Therefore, this model can be used to analyze the original system using known systems analysis techniques. In this paper a methodology for extract information from unknown systems using fuzzy logic is presented. More precisely, it is presented the exact linearization of a Takagi–Sugeno fuzzy model with no restrictions in use or distribution of its membership functions, as well as obtaining its equilibrium states, the study of its local behavior and the search for periodic orbits by the application of Poincaré.

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References

  • Abraham, R. H., & Shaw, C. D. (1997). Dynamics: The geometry of behavior. Santa Cruz: Aerial Press, Incorporated.

    Google Scholar 

  • Al-Hadithi, B. M., Jiménez, A., Matía, F., Andújar, J. M., & Barragán, A. J. (2014). New concepts for the estimation of Takagi–Sugeno model based on extended Kalman filter. In F. Matía, G. N. Marichal, & E. Jiménez (Eds.), Fuzzy modeling and control: Theory and applications, atlantis computational intelligence systems (Vol. 1, pp. 3–24). Paris: Atlantis Press.

    Google Scholar 

  • Andújar, J. M., & Barragán, A. J. (2005). A methodology to design stable nonlinear fuzzy control systems. Fuzzy Sets and Systems, 154(2), 157–181.

    Article  MathSciNet  Google Scholar 

  • Andújar, J. M., Barragán, A. J., Al-Hadithi, B. M., Matía, F., & Jiménez, A. (2014). Suboptimal recursive methodology for Takagi–Sugeno fuzzy models identification. In F. Matía, G. N. Marichal, & E. Jiménez (Eds.), Fuzzy modeling and control: Theory and applications, Atlantis computational intelligence systems (Vol. 2, pp. 25–47). Paris: Atlantis Press.

    Google Scholar 

  • Andújar, J. M., & Bravo, J. M. (2005). Multivariable fuzzy control applied to the physical–chemical treatment facility of a cellulose factory. Fuzzy Sets and Systems, 150(3), 475–492.

    Article  MathSciNet  Google Scholar 

  • Andújar, J. M., Bravo, J. M., & Peregrín, A. (2004). Stability analysis and synthesis of multivariable fuzzy systems using interval arithmetic. Fuzzy Sets and Systems, 148(3), 337–353.

    Article  MathSciNet  Google Scholar 

  • Barragán, A. J., Al-Hadithi, B. M., Jiménez, A., & Andújar, J. M. (2014). A general methodology for online TS fuzzy modeling by the extended Kalman filter. Applied Soft Computing, 18, 277–289.

    Article  Google Scholar 

  • Barragán, A. J., & Andújar, J. M. (2012). Fuzzy logic tools reference manual v1.0. University of Huelva. http://uhu.es/antonio.barragan/flt

  • Bezdek, J. C., Ehrlich, R., & Full, W. E. (1984). FCM: The fuzzy c-means clustering algorithm. Computers and Geosciences, 10(2–3), 191–203.

    Article  Google Scholar 

  • Cazarez-Castro, N. R., Aguilar, L. T., Cardenas-Maciel, S. L., Goribar-Jimenez, C. A., & Odreman-Vera, M. (2017). Design of a fuzzy controller via fuzzy Lyapunov synthesis for the stabilization of an inertial wheel pendulum. Revista Iberoamericana de Automática e Informática Industrial (RIAI), 14(2), 13–140.

    Google Scholar 

  • Dorigo, M., Di Caro, G., & Gambardella, L. M. (1999). Ant algorithms for discrete optimization. Artificial Life, 5(2), 137–172.

    Article  Google Scholar 

  • González Fontanet, J. G., Lussón Cervantes, A., & Bausa Ortiz, I. (2016). Alternatives of control for a Furuta’s pendulum. Revista Iberoamericana de Automática e Informática Industrial (RIAI), 13(4), 410–420.

    Article  Google Scholar 

  • Grande, J. A., Andújar, J. M., Aroba, J., Beltrán, R., de la Torre, M. L., Cerón, J. C., et al. (2010). Fuzzy modeling of the spatial evolution of the chemistry in the Tinto River (SW Spain). Water Resources Management, 24(12), 3219–3235.

    Article  Google Scholar 

  • Horikawa, S. I., Furuhashi, T., & Uchikawa, Y. (1992). On fuzzy modeling using fuzzy neural networks with the back-propagation algorithm. IEEE Transactions on Neural Networks, 3(5), 801–806.

    Article  Google Scholar 

  • Jang, J. S. R. (1993). ANFIS: Adaptive-network-based fuzzy inference system. IEEE Transactions on Systems, Man, and Cybernetics, 23(3), 665–685.

    Article  Google Scholar 

  • Khalil, H. K. (2000). Nonlinear systems. Upper Saddle River, NJ: Prentice-Hall.

    MATH  Google Scholar 

  • Kóczy, L. T., & Hirota, K. (1997). Size reduction by interpolation in fuzzy rule bases. IEEE Transactions on Systems, Man, and Cybernetics-Part B: Cybernetics, 27(1), 14–25.

    Article  Google Scholar 

  • Kreinovich, V., Hguyen, H. T., & Yam, Y. (2000). Fuzzy systems are universal approximators for a smooth function and its derivatives. International Journal of Intelligent Systems, 15(6), 565–574.

    Article  Google Scholar 

  • Levenberg, K. (1944). A method for the solution of certain problems in least squares. Quarterly of Applied Mathematics, 2, 164–168.

    Article  MathSciNet  Google Scholar 

  • Li, S. Y., & Yang, Y. P. (2003). On-line constrained predictive control algorithm using multi-objective fuzzy-optimization and a case study. Fuzzy Optimization and Decision Making, 2(2), 123–142.

    Article  MathSciNet  Google Scholar 

  • López-Baldán, M. J., García-Cerezo, A., Cejudo, J. M., & Romero, A. (2002). Fuzzy modeling of a thermal solar plant. International Journal of Intelligent Systems, 17(4), 369–379.

    Article  Google Scholar 

  • Márquez, J. M. A., Piña, A. J. B., & Arias, M. E. G. (2009). A general and formal methodology for designing stable nonlinear fuzzy control systems. IEEE Transactions on Fuzzy Systems, 17(5), 1081–1091.

    Article  Google Scholar 

  • McCulloch, W. S., & Pitts, W. (1943). A logical calculus of the ideas immanent in nervous activity. The Bulletin of Mathematical Biophysics, 5(4), 115–133.

    Article  MathSciNet  Google Scholar 

  • Mora, L. A., & Amaya, J. E. (2017). A new identification method based on open loop step response of overdamped system. Revista Iberoamericana de Automática e Informática Industrial (RIAI), 14(1), 31–43.

    Article  Google Scholar 

  • Penedo, F., Haber, R. E., Gajate, A., & del Toro, R. M. (2012). Hybrid incremental modeling based on least squares and fuzzy \(K\)-NN for monitoring tool wear in turning processes. IEEE Transactions on Industrial Informatics, 8(4), 811–818.

    Article  Google Scholar 

  • Shin, H., Choi, C., Kim, E., & Park, M. (2004). Fuzzy partial state feedback control of discrete nonlinear systems with unknown time-delay. Fuzzy Optimization and Decision Making, 3(1), 83–92.

    Article  MathSciNet  Google Scholar 

  • Shouyu, C., & Yu, G. (2006). Variable fuzzy sets and its application in comprehensive risk evaluation for flood-control engineering system. Fuzzy Optimization and Decision Making, 5(2), 153–162.

    Article  MathSciNet  Google Scholar 

  • Slotine, J. J. E., & Li, W. (1991). Applied nonlinear control. Upper Saddle River, NJ: Prentice-Hall.

    MATH  Google Scholar 

  • Takagi, T., & Sugeno, M. (1985). Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Systems, Man, and Cybernetics, 15(1), 116–132.

    Article  Google Scholar 

  • Vélez, M. A., Sánchez, O., Romero, S., & Manuel, A. J. (2010). A new methodology to improve interpretability in neuro-fuzzy TSK models. Applied Soft Computing, 10(2), 578–591.

    Article  Google Scholar 

  • Wang, L. X. (1992). Fuzzy systems are universal approximators. In IEEE international conference on fuzzy systems, San Diego, CA, USA (pp. 1163–1170).

  • Wang, L. X. (1994). Adaptive fuzzy systems and control. Upper Saddle River, NJ: Prentice Hall.

    Google Scholar 

  • Wong, L., Leung, F., & Tam, P. (1997). Stability design of TS model based fuzzy systems. In IEEE international conference on fuzzy systems, Barcelona, Spain (Vol. 1, pp. 83–86).

  • Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.

    Article  MathSciNet  Google Scholar 

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Acknowledgements

This work is a contribution of the DPI2015-71320-REDT Project supported by the Spanish Ministry of Economy and Competitiveness.

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Authors and Affiliations

  1. Department of Electronic Engineering, Computer Systems and Automatic, Universidad de Huelva, Huelva, Spain

    A. Javier Barragán, Juan M. Enrique & José M. Andújar

  2. Department of Electrical, Electronic and Automatic Engineering, Universidad de Extremadura, Badajoz, Spain

    Antonio J. Calderón

Authors
  1. A. Javier Barragán
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  2. Juan M. Enrique
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  3. Antonio J. Calderón
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  4. José M. Andújar
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Correspondence to A. Javier Barragán.

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Javier Barragán, A., Enrique, J.M., Calderón, A.J. et al. Discovering the dynamic behavior of unknown systems using fuzzy logic. Fuzzy Optim Decis Making 17, 421–445 (2018). https://doi.org/10.1007/s10700-018-9285-4

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